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I read two sentences that makes me very unsure to what does but refer to. I am really confused, does but refer to the old method (Kim et al. (2013)) or to the new method.

"Our modelling strategy is related to the work of Kim et al. (2013) and their idea of using mixtures of D-vines but tackles the problem of constructing a vine model from a different perspective."

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"But" doesn't refer. The two predicates which are conjoined are "is related ... D-vines" and "tackles ... perspective". These are both predicated of the subject "Our modelling strategy".

The only significance of using "but" rather than "and" is that the sentence is making an explicit or implicit contrast. Here the contrast is that it tackles the problem not the same way as Kim et al, but in the new way described.

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Supplemental to Colin Fine's excellent answer.

Both and and but are co-ordinating conjunctions. And is a cumulative conjunction which adds one statement to another whereas but expresses opposition or contrast between two statements.

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